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How to Calculate the Volume of Shaded Regions of Cylinders

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Tags:Calculate Volume of Shaded Regions of Cylinders,how to calculate the volume cylinders,how to calculate the volume of shaded regions of c,math help,math measurements,Math Study Tips,measurement help,tenmarks,what is the volume of a cylinder

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Transcript

In this video lesson, let’s learn about volume of shaded regions when it comes to cylinders. We’re given a diagram of a cylinder which has a shaded region and we have to find the volume of the shaded cylinder to the nearest cubic unit and we have to use pi=3.14.

Note the dimensions of the cylinder, we have the big outer cylinder and the dimension so of the outer cylinder are, well, we are given that the height is 14 feet and the diameter is given to us as 10 feet, that’s the diameter or the base. So the diameter equals 10 feet. Then we have the inner cylinder because the empty hole, the hallow portion in the middle is a cylinder as well. The inner cylinder has got the same height because the hallow area goes through the cylinder but the diameter of this is not given to us but we’re given that this part is 3 feet and this part is 3 feet. So if the total part is 10 feet, that’s the total diameter, then I can say that the diameter of the inside part equals 10 feet – 3 – 3 which is 4 feet. Because of this entire or this entire diameter is 10 feet, I can subtract 3 from the side and 3 from the side so this part is 4 feet.

So if we need to compute the volume of the shaded area of the cylinder, then the volume of the shaded are equals the volume of the outer area, the outer cylinder, minus volume of the inner cylinder. All we’re doing is computing the volume of the entire cylinder and removing or subtracting from it the volume of the inner cylinder which is the hallow part. So let’s do that.

What is the formula to use? The formula for the volume of a cylinder equals pi x r2 x h. That’s for us to remember. So let’s compute the outer cylinder. Let’s look at the outer cylinder. What’s the volume? What’s given to us? If the diameter equals 10 feet, that means that radius equals 5 feet. Here, if the diameter equals 4 feet, the radius equals 2 feet because radius is always half the diameter. So the volume of the outer cylinder is 3.14 which is the value of pi, v equals 3.14 times radius squared. Radius is 5 feet, and then we have multiplied by height which is 14 feet. What does that mean? So 3.14 x 25 ft2 x 14 ft, or if I multiply 3.14 x 25, that gives me 78.5 approximately, times 14 feet cubed, because feet squared times feet will give us the unit of feet cubed.

Let’s go down a little bit, so the volume of the outer cylinder will be 78.5 x 14 which is approximately 1099 ft3. So that’s equal to—let’s use approximately because that’s what we’re approximately trying to do.

Now, let’s look at the second part which is the volume of the inner cylinder. Same formula, so the volume of the inner cylinder would be 3.14 which is the value of pi times the radius which is 22 times the height which is 14 feet. Again, 3.14 multiplied by 4 multiplied by 14 ft3. So 3.14 x 4 is 12.56 multiplied by 14 ft3 , taking a little bit more space, I got 12.56 multiplied by 14 which is 175.84 ft3. So the volume of the inner cylinder is 175.84 ft3.

So now, to compute the difference between them, I simply have to subtract these two. So the volume of the shaded area is 1099-176 which is approximately 923 ft3. The volume of the shaded part of the cylinder is 9.23 ft3. That’s what we were looking for.

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